Noget er råddent i staten Danmark.
Has Hamlet been translated into Danish? It must have been at some point, right? It just seems far too appropriate for it to not have happened, and that's before taking into consideration that Shakespeare is surely a popular choice for translating. Right?
In the Danish TV series 1864 (which is on BBC iPlayer for anyone in the UK) there is a scene where they watch Hamlet being performed in Danish. I recommend Danish learners watch 1864 by the way, it's good and because they are in 'the olden days' they seem to speak more clearly and with less confusing slang than other Danish programs I've watched. So it's really good practice!
You have more faith in Google understanding of sentences... I kinda go from the assumption of brute keyword search. Sentences like "Hamlet, in the play, is a Danish prince..." or "Kastrup, a delightful hamlet in the Danish countryside..." would match Hamlet+in+Danish as well. May the google be with you!
Another angle is that Shakespeare translated/plagerised the story of "Amlet"/"Amled"/"Amleth" in Saxo Gramaticus' "Gesta Danorum" (written in Latin) into his famous play Hamlet. "Gesta Danorum" is a famous collection of the history (stories) about the Danish royal linage. Some of the persons mentioned in the book have been verified as real people (e.g. Gorm the Old), but some of the people from the earliest part of the book come across as legends.
Saxo Gramaticus in English on project Gutenberg: http://www.gutenberg.org/files/1150/1150-h/1150-h.htm See book three and search for "aml" in the page to find the original story about Hamlet.